The line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 1 2, then the intersection with the domain is r = -5/3.
The line that passes through the pair of points has the given slope is,
( − 2 , 8 ) , ( r , 4 ) and m = -12
What is Slope :Slope, numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
m = rise/run
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Where,
m = slope
[tex](x_{1} ,y_{1} )[/tex] = coordinates of first point in the line
[tex](x_{2} ,y_{2} )[/tex] = coordinates of second point in the line
Then, we can find the [tex]m_{1}[/tex]
We can use these two values, ( − 2 , 8 ) , ( r , 4 )
x1 = -2
y1 = 8
x2 = r
y2 = 4
m = [tex]\frac{4-8}{r-(-2)}[/tex]
[tex]m = \frac{-4}{r+2}[/tex]
We can substitute m= -12 value into m= -(4/r+2)
So,
We can write,
-12 = [tex]\frac{-4}{r+2}[/tex]
We can find the domain,
If the fraction is defined, the dominator can not be equal to zero.
2 + r ≠ 0
Rearrange variables to the left side of the inequality,
r ≠ -2
Append the inequality as the domain,
r ≠ -2
We can solve the equation,
-12 = [tex]\frac{-4}{r+2}[/tex]
Multiply both sides of equation by the common denominator,
-12 (r+2) = -4(r+2)/ (r+2)
Reduce the fractions,
-12 (r+2) = -4
Apply the distributive property,
-12r - 24 = -4
Rearrange variable to the left side of the equation,
-12r = -4 + 24
Calculate the sum or difference,
-12r = 20
Divide both sides of the equation by the coefficient of variables,
r = - 20/12
r = -5/3
Therefore,
The intersection with the domain is r = -5/3, so the line that passes through the pair of points has the given slope. ( − 2 , 8 ) , ( r , 4 ) , m = − 12.
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A new television set was recently purchased for the common room in a residence hall for $520.00 including tax. If the tax rate is 4%, find the price of the television set before taxes.
Let's use the variable x to represent the price of the television set before taxes.
If the tax rate is 4%, then the original price is multiplied by 1.04, so it is equal 1.04x.
The final price is $520, so we have:
[tex]\begin{gathered} 1.04x=520 \\ x=\frac{520}{1.04} \\ x=500 \end{gathered}[/tex]So the price before taxes is $500.00.
Find the measure of each arc. For each arc, write two or more complete sentences explaining which theorem or postulate you used to find your answer. Include your equations and calculations in your final answer.
m arcRPQ
Answer:
arc RPQ = 305°
Step-by-step explanation:
• the angle at the centre is equal to the measure of the arc that subtends it.
arc RP = ∠ ROP = 125°
∠ QOS and ∠ ROP are vertically opposite angles and are congruent, so
∠ QOS = 125° and so arc SQ = 125°
RS is a straight angle , then
∠ POS = 180° - 125° = 55°
arc PS = 55° ( arc subtending the angle at centre
Then
arc RPQ = RP + PS + SQ = 125° + 55° + 125° = 305°
"if i flip a coin, i have a 50 percent chance that it will land on heads." in this statement, even after the first coin flip, we still have a 50 percent chance that the next flip will result in a head. this statements interprets "probability" as:
The probability of getting heads on both occasions will be 0.25.
How to calculate the probability?It should be noted that probability simply means the likelihood that a particular event will happen.
In this case, if I flip a coin, i have a 50 percent chance that it will land on heads and after the first coin flip, we still have a 50 percent chance that the next flip will result in a head.
The probability will be:
= P(head) × P(head)
= 50% × 50%
= 1/2 × 1/2
= 1/4
= 0.25
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Use the following function rule to find f(2).
f(x) = 4 + x
f(2)=
Please quickly help me figure this out
The final expression of the simplified version is 28x + 8y + 2.
What is the simplified version?We know that, to simplify means to obtain the lowest possible form of the of the expression. The expression is written in its simplest form when there are no more ambiguities left in the way that it is written.
Given the expression;
-2(3x + 12y - 5 - 17x - 16y + 4)
We can now expand the expression to have;
-6x - 24y + 10 + 34x + 32y - 8
This could further simplify to
-6x + 34x - 24y + 32y + 10 - 8
To obtain the final simplified expression, we have;
28x + 8y + 2
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Use the Law of Detachment to make a conclusion. If a person wants to get a car, that person must buy car insurance. Jayla wants to get a car. A. Jayla has car insurance. B. Jayla has her driver's license. C. Jayla must get her driver's license. D. Jayla must buy car insurance.
According to the law of detachment, if a person wants to get a car, that person must buy car insurance, since Jayla wants to get a car, D. Jayla must buy car insurance.
What is the law of detachment?It should be noted that the law of detachment states that if P leads to Q and Q is true, then Q must be true.
In this case, if a person wants to get a car, the person must buy car insurance. Without this it's impossible to buy the car. Therefore, this illustrates that the correct option is that Kayla must also get the insurance.
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Mia sells headbands for $8.50 each. The
situation can be represented by y = 8.50x
where x is the number of headbands sold and
y is the amount of money collected. Does this
situation represent a function?
Answer:
Yes
Step-by-step explanation:
This is a linear function, which you can see if you graph it. It is in the form of y = mx + b where be = 0 and the slope is 8.5.
Toilet rolls come in a pack of 4 and 9 the 4-pack is priced at £2.04 and the 9- pack is priced at £4.68 . By calculating the price per roll, determine which pack is better value
4pack price plus 9pack price
so it implies that 2.o4+4.68=6.72
15≥3x-3>-12
What would the answer to this be
Answer:
-3 < x ≤ 6
(-3, 6]
Step-by-step explanation:
15 ≥ 3x - 3 > -12
+3 +3 +3
------------------------
18 ≥ 3x > -9
÷3 ÷3 ÷3
-------------------
6 ≥ x > -3
-3 < x ≤ 6
(-3, 6]
I hope this helps!
whats the answer to this combined terms
y−(−3y)
Answer:
Add y and 3y
= 4y
Step-by-step explanation:
The graph shows the temperature of ice cream in an ice chest during an overnight trip. What is the domain of this function?
The domain is negative 10 through 30.
The domain is all integers from negative 10 through 30.
The domain is all real numbers 0 through 30.
The domain is all integers from 0 through 30.
The domain of this function is that: C. the domain is all real numbers 0 through 30.
What is a domain?A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
How to identify the domain of this graph?The horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
By critically observing this graph of a function shown, we can reasonably infer and logically deduce the following:
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Select whether ←→ A B and ←→ C D are parallel, perpendicular, or neither. Graph each line on a separate sheet of paper to verify your answer. A ( − 6 , − 9 ) , B ( 8 , 19 ) , C ( 0 , − 4 ) , D ( 2 , 0 )
The slope of AB = 2
The slope of CD = 2
Both lines are parallel lines.
How to Determine Parallel and Perpendicular Lines?The lines that are perpendicular to each other have slope values that are negative reciprocal of each other.
For example, if the a line's slope is a, the line that is perpendicular to it will have a slope of -1/a. This is because the negative reciprocal of a is -1/a, and (a)(-1/a) = -1.
On the other hand, the lines that are parallel to each other will have the same slope value.
Given the following:
A(−6 , −9)
B(8, 19)
C(0, −4)
D(2, 0)
Find the slope (m) of AB:
Slope of AB = (19 -(-9))/(8 -(-6))
Slope of AB = 28/14
Slope of AB = 2
Find the slope (m) of CD:
Slope of CD = (0 -(-4))/(2 - 0)
Slope of CD = 4/2
Slope of CD = 2
The graph of both lines are shown below.
Thus, the slope of AB and CD are the same, therefore, we can conclude that lines AB and CD are parallel to each other.
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AN IRRATIONAL VALUE
GREATER THAN 5
A. √75
B. 5.9
C. 5pi
D. 5
From the given options,√75 and 5π are the irrational numbers with a value greater than 5.
What exactly is an irrational number?Irrational numbers are real numbers that cannot be represented as simple fractions. It cannot be expressed mathematically.
How can you tell whether a number is rational or irrational?A rational number is one that can be written as P/Q, where P and Q are integers and Q is not equal to 0. However, an irrational number cannot be written in simple fractions.We need to find an irrational value which is greater than 5 from the options given as follows:
A. √75
B. 5.9
C. 5pi
D. 5
Options B and D are not irrational numbers so both are incorrect options.
For Option A,
[tex]\sqrt{75}[/tex] = 8.66
For Option C,
5π = 15.70
We can see that both options A and C have irrational value greater than 5.
As a result, from the options given,√75 and 5π are irrational numbers with a value greater than 5.
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what transformations take f(x) = 3x+1 to g(x) = −3x−5 ?
options:
A. a reflection over the x-axis and a translation 4 units up
B. a reflection over the x-axis and a translation 4 units down
C. a reflection over the y-axis and a translation 4 units up
D. a reflection over the y-axis and a translation 4 units down
The correct transformation for f(x) = 3x+1 to g(x) = −3x−5 is a reflection over the y-axis, and a translation 4 units down. Option D
This is further explained below.
What is transformation?A point, line, or geometric figure may be transformed in one of four ways, each of which affects the shape and/or location of the object.
Pre-Image refers to the object's initial shape, while Image, after transformation, refers to the object's ultimate shape and location.
Generally, the equation for the function is mathematically given as
f(x) = 3x+1
The transformed function
g(x) = −3x−5
In conclusion, The transformations consist of Reflection along the y-axis.
The translation of down four units
Hence, a reflection over the y-axis, and a translation 4 units down. Option D
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Kylie just accepted a job at a new company where she will make an annual salary of $67000. kylie was told that for each year she stays with the company, she will be given a salary raise of $3000. how much would kylie make as a salary after 3 years working for the company? what would be her salary after tt years?
Since the situation can be since as an arithmetic sequence, her salary after 3 years is $73,000. After t years, her salary is a function of t, that is a(t) = 64000 + 3000 t
The given situation can be seen as an arithmetic sequence. The nth term of an arithmetic sequence is given by the formula:
a(n) = a(1) + (n - 1) . d
Where:
a(1) = the first term
d = the common difference.
The problem can be translated into an arithmetic sequence with:
a(1) = $67000
d = $3000
Kylie's salary after 3 years is a(3),
a(3) = a(1) + (3 - 1) . d
a(3) = Kylie's salary + 2 . 3000 = 73000
Hence, after 3 years, Kylie's salary is $73,000
Her salary after t years, means n = t. Therefore,
a(t) = a(1) + (t - 1) . d
a(t) = 67000 + (t -1) . 3000
a(t) = 64000 + 3000 t
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what is the equation of a line that is parallel to line y=3x+5 and goes through the point (6,-7)
The equation of a line that is parallel to line y=3x+5 and goes through the point (6,-7) is y = 3x + 2
What is equation of line ?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line. Any line's equation can be used to determine whether a given point is on the line or not.A linear equation with a degree of one is the equation for a line.
Given that : the equation of a line is parallel to line y=3x+5 and goes through the point (6,-7)
y=3x+5 is the equation for the given line.
This type of line is called a slope intercept. The line has a slope of m=3.
The slope of parallel lines is equal. As a result, all lines with slope m=3 will be perpendicular to one another.
y=3x+2 is an example of a line that is parallel to the supplied line.
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Malia put 12 photos into an album. She split the photos evenly among p pages. Write an expression that shows how many photos are on each page.
hey yall my question is: how do u divide 5 600 in the ratio:
4: 5: 7
:)
explanation
4/16×5600=1400
5/16×5600=1750
7/16×5600=2450
therefore first ratio over total ratio multiplied by number. use the same approach for the others
Pls help!!
Using the following graph, write the equation of a line that is parallel to the given line and passes through the point (0, 0).
(Write your answer is slope intercept form. The y= is already typed for you, so only type the remainder of the equation using NO spaces!)
Answer:
0
Step-by-step explanation:
because the rule says have u understand
complete the table of values for y = 1 over x
The table of values for the given equation, y = 1/x, is
x y
-3 -1/3
-2 -1/2
-1 -1
0 ∞
1 1
2 1/2
3 1/3
Table of values of an equationFrom the question, we are to determine the table of values for the given function
The given equation is y = 1/x
We will determine the values of y for certain values of x
When x = -3
y = 1/x
y = 1/-3
y = -1/3
When x = -2
y = 1/x
y = 1/-2
y = -1/2
When x = -1
y = 1/x
y = 1/-1
y = -1
When x = 0
y = 1/x
y = 1/0
y = ∞
When x = 1
y = 1/x
y = 1/1
y = 1
When x = 2
y = 1/x
y = 1/2
When x = 3
y = 1/x
y = 1/3
Thus,
The table of values is
x y
-3 -1/3
-2 -1/2
-1 -1
0 ∞
1 1
2 1/2
3 1/3
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help me i don’t know how to do this help me please
The speed limit on a road is listed at 65 miles per hour. The car’s speedometer reads 63 miles per hour. Is it possible that this car is going over the speed limit?
It is not possible for the car to go over the speed limit as maximum error represent value of speed limit less than 65 miles per hour.
As given in the question,
Maximum error on the reading of speedometer =1.6%
Speed limit on a road is 65 miles per hour
Reading of a speedometer = 63 miles per hour
As per the error in the speedometer it can be more or less by 1.6%
To check speed limit
If it more
Speed limit = 63 + (1.6% of 63)
= 63 + 1.008
= 64.008 miles per hour < 65 miles per hour
If it less
Speed limit = 63 - (1.6% of 63)
= 63 -1.008
= 61.992 miles per hour < 65 miles per hour
Therefore, it is not possible for the car to go over the speed limit as maximum error represent value of speed limit less than 65 miles per hour.
The complete question is:
The reading on a car speedometer has 1.6% maximum error the speed limit on a road is listed 65 miles per hour.
The car’s speedometer reads 63 miles per hour. Is it possible that this car is going over the speed limit?
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Alice, raul, and jane are baking cookies together, alice brought 2.5 cups of flour, raul brought 1 1/4 cups of flour and jane brought 3/4 cups of flour. how many cups of flour they have all together? show all work.
The total cups of flour Alice, Raul and Jane have altogether is equal to 6.
We can determine the number of cups of flour they have all together by the addition of the fractions brought by each one of them.
First, we convert the decimal value of 2.5 into fraction form;
2.5 = 2.5/1
Multiplying and dividing both sides by 10;
25/10 = 5/2
Now we add the fractions as follows;
Total number of cups of flour = 5/2 + 11/4 + 3/4
We Multiply 5/2 by 2 to get the same denominator as the other values;
5×2 / 2×2 = 10/4
10/4 + 11/4 + 3/4 = 6
Therefore, the total number of cups of flour they have altogether is calculated to be 6.
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A bike was reduced by 20% in a sale. If it was £520 what was the original price
Answer:416
Step-by-step explanation:520x.8=416
Answer:
Original price = 416.
i hope this helps
29 less than -10 times a number is equal to -18 times the number plus 91
Answer:
-10x - 29 = -18x + 91
x = 15
Step-by-step explanation:
29 less than -10 times a number is equal to -18 times the number plus 91:
-10x - 29 = -18x + 91
add 21 to both sides:
-10x - 29 + 29 = -18x + 91 + 29
-10x = -18x + 120
add 18x to both sides:
-10x + 18x = -18x + 120 + 18x
8x = 120
divide both sides by 8:
8x/8 = 120/8
x = 15
write a mathematical sentence that expresses the information below use s as your variable mr.jones algebra class has too many students in it. if each class were split exactly
When the class were split exactly in equal parts to form 3 be classes each class would have no more than 14 students, the expression is s / 3 <= 14.
What is an expression?It should be noted that an expression is simply used to illustrate the relationship between the variables that are given.
From the mr. Jones algebra class has too many students in it and each class were split exactly in equal parts to form 3 be classes each class would have no more than 14 students.
The expression will be let the total students be represented by s. This will be:
s / 3 <= 14
The expression is s / 3 <= 14.
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Write a mathematical sentence that expresses the information below use s as your variable mr.jones algebra class has too many students in it. if each class were split exactly in equal parts to form 3 be classes each class would have no ore than 14 students
5. Please verify correct
Our function is a parabola, therefore, it has only one critical point which is its vertex. Since the coefficient of the squared term is negative, the vertex is the maximum point.The critical points of a function are given by the zeros of the first derivative. The first derivative of our function is:
[tex]f^{\prime}(x)=-6x-18[/tex]The solutions for the following equation are the critical points of the original function:
[tex]-6x-18=0\implies x=-3[/tex]The maximum point happens at x = - 3.
To find the corresponding value, we just have to evaluate x = - 3 into our function:
[tex]f(-3)=-3(-3)^2-18(-3)-26=1[/tex]The maximum value of the function is 1, and it occurs at x = - 3.
Answer: The function has a maximum value
The function's maximum value is 1
The function's maximum value occurs at x=-3
Step-by-step explanation:
Given equation: [tex]g(x) = -3x^ - 18x - 26[/tex]
We shall use the differentiation method to find the answer.
Differentiating the equation, we get [tex]g'(x) = - 6x - 18[/tex]
equating g'(x) = 0,
[tex]-6x - 18 = 0\\-6x = 18 \\x = -3[/tex]
Hence the minimum/ maximum value of the function lies in x = -3
on equating x>-3, g'(x) is negative
on equating x<-3, g'(x) is positive
this proves that first, the function was increasing and after x = -3, the function started to decrease hence at x=-3, the function g(x) was at its maximum value
The function's maximum value at x=-3 is
[tex]g(x) = -3x^2 - 18x - 26\\g(-3) = -3(-3)^2 - 18(-3) - 26\\g(-3) = -3(9) +54 -26\\g(-3) = 54 - 27 -26\\g(-3) = 1[/tex]
All of the following expressions represent the sum of n and itself, except.
O2n
On²
On+n
All of the following expressions represent the sum of n and itself, except n²
To solve his problem, we need a brief idea about algebraic operations like summation, multiplication, etc.
When we add two or more same algebraic digits we have to just add their coefficients. Otherwise, it remains the same.
Example :
x + 2x + 4x = 6x [ 1 + 2 + 4 = 7; as 1,2,4 are the coefficient of x, 2x, 4x ] x + 2y + z = x + 2y + z ( remains unchanged as they all are different numbered )Here 2n = n + n, the sum of n and itself but n² = n × n, which is the multiplication of n and itself,
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i need help with this question 20 points
Answer:
I think the answers are the last two.
Step-by-step explanation:
A rational number is any faction with a denominator not being 0. For example, 1/2, 1/5, 3/6, etc. Also, the number 0 is also a rational number.
If you think any other ones are also the answer, just use my explanation to help it clear stuff up. :)
Guys help!!! I have to create a other title for the book The call of the wild. Help me figure out titles I should use and why. Write a well-developed paragraph explaining why the title you have chosen suits the book.
You do not need to listen to my opinion but I think another excellent title could be Survival (Man Vs Dog).
And so here is an explanation of this title: The book may be for young adults, but it truly shows a dark trip to human nature and a species that can be noble as well as cruel and insensitive. Buck, the protagonist, is a dog who has been kidnapped and placed as a sled dog in the 19 century Klondike Gold Rush. It is Buck's loyalty and instinct that helps him return to his owners which forms the plot of the story and the assumptions are able to make about the inhumanity of humans and the very real loyalty and humanity Buck shows.
Sorry for taking so long:)